1.13. FLUID81 - Axisymmetric-Harmonic Contained Fluid

Matrix or Vector	Geometry	Shape Functions	Integration Points
Stiffness and Damping Matrices; and Thermal Load Vector	Quad	Equation 11–164, Equation 11–165, and Equation 11–166	1 for bulk strain effects 2 x 2 for shear and rotational resistance effects
Stiffness and Damping Matrices; and Thermal Load Vector	Triangle	Equation 11–156, Equation 11–157, and Equation 11–158	1 for bulk strain effects 3 for shear and rotational resistance effects
Mass Matrix	Quad	Equation 11–122, Equation 11–123, and Equation 11–124	2 x 2
Mass Matrix	Triangle	Equation 11–101, Equation 11–103, and Equation 11–104	3
Pressure Load Vector	Same as stiffness matrix, specialized to the face		2

Load Type	Distribution
Element Temperature	Average of the four nodal temperatures is used throughout the element
Nodal Temperature	Same as element temperature distribution
Pressure	Linear along each face

1.13.1. Other Applicable Sections

Structures describes the derivation of element matrices and load vectors. The fluid aspects of this element are the same as described for FLUID80 - 3D Contained Fluid except that a consistent mass matrix is also available (LUMPM,OFF).

1.13.2. Assumptions and Restrictions

The material properties are assumed to be constant around the entire circumference, regardless of temperature dependent material properties or loading.

1.13.3. Load Vector Correction

When (input as MODE on MODE command) > 0, the gravity that is required to be input for use as a gravity spring (input as ACELY on ACEL command) also is erroneously multiplied by the mass matrix for a gravity force effect. This erroneous effect is cancelled out by an element load vector that is automatically generated during the element stiffness pass.